Resonant frequency of a LCR series circuit is 16 kHz. If the capacitance is increased to 16 times, then the new resonant frequency will become
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 4 kHz
$\text{Given: Initial resonant frequency } f_0 = 16~\text{kHz}$
$\text{Capacitance increased to 16 times: } C_\text{new} = 16 C$
$\text{Resonant frequency of LCR series: } f = \frac{1}{2 \pi \sqrt{L C}}$
$f_\text{new} = \frac{1}{2 \pi \sqrt{L C_\text{new}}} = \frac{1}{2 \pi \sqrt{L \cdot 16 C}} = \frac{1}{4 \pi \sqrt{L C}} = \frac{f_0}{4}$
$f_\text{new} = \frac{16~\text{kHz}}{4} = 4~\text{kHz}$
$\text{Answer: } f_\text{new} = 4~\text{kHz}$